I am interested in testing a path model with two ordinal variables predicting a count variable (range = 0-90). I must choose between the poisson and zero-inflated poisson distributions. To make this choice, I would like to test for overdispersion using MPlus if at all possible.

Is it possible to test for overdispersion within Mplus? If so, could you provide a step-by-step regarding how to do so?

"You can run it both ways and see which model has the best loglikelihood"

I was hoping for a method that could test the statistical significance of the difference in loglikelihood between these two models (e.g., likelihood ratio test). My understanding is that the poisson and zip models are not nested, so typically the difference in fit between these models is evaluated using the vuong statistic. Is this approach possible using Mplus?

"If the model with inflation has an inflation constant of -15, then you don't need inflation."

Could you please explain what the inflation constant signifies and why a cutoff of -15 would lead one to favor the poisson moodel? Secondly, is this a heuristic or is this cutoff based on research? Relatedly, how would one defend this decision?

The Mplus User's Guide describes this modeling in examples 7.2 and 7.25. Ex 7.2 describes the inflation matter in Mplus terms. You see there that "the binary inflation variable u#1 --- describes the probability of being unable to assume any value except zero". This is talking about being in the inflation class. So when the mean (or intercept) in the logit scale goes large negative (-15 say), you find that the probability of being in the inflation class is essentially zero.

The Poisson and the ZIP are nested as far as I understand, but with the caveat that you have Poisson as a special case with the probability of being in the inflation class being zero - so not fulfilling the LR chi-square requirement of parameters being within the admissible space. If you do ZIP analysis as in 7.25 you work with 2 classes and therefore it would seem that you can instead use the Vuong approach of testing k-1 vs k classes, which is Tech11 in Mplus, or a bootstrapped LRT approach, which is Tech14 in Mplus. These approaches are described in the User's Guide and also applied in latent class settings in the Nylund et al paper on our web site under Recent Papers. Note that Mplus deletes the first class in testing k-1 vs k classes, so you want to put the inflation class first. I have not tested out this approach, however.

Is there a way to have an overdispersion parameter in a multilevel logistic model in Mplus? This is possible in SAS GLIMMIX as applied to binary outcomes. As far as I have been able to find in the Mplus manual and in output, a dispersion parameter can only be requested for the count outcomes.